FACULTY OF APPLIED SCIENCES DEPARTMENT OF CIVIL ENGINEERING DIVISION OF STRUCTURAL MECHANICS KASTEELPARK ARENBERG 40 B-3001 HEVERLEE BELGIUM
KATHOLIEKE UNIVERSITEIT LEUVEN
Status
TEUGHELS,A. and DE ROECK,G., Improvement of the general FEM updating method by the use of damage functions, EUROMECH Colloquium 437: Identification and updating methods of mechanical structures, Prague, Czech Republic, June, 2002
IR.ARCH. A. TEUGHELS TEL. (+32 16)32 16 77 FAX (+32 16)32 19 88 E-mail: anne.teughels@bwk.kuleuven.ac.be http://www.bwk.kuleuven.ac.be/bwm/
Improvement of the general FEM Updating method by the use of damage functions
A. Teughels and G. De Roeck
Department of Civil Engineering, K.U.Leuven Division of Structural Mechanics Kasteelpark Arenberg 40, 3001 Heverlee, Belgium e-mail: Anne.Teughels@bwk.kuleuven.ac.be
In Finite Element Model (FEM) updating the uncertain physical parameters of the structure are adapted such that the differences between the numerical and experimental vibration data are minimised [1]. In civil engineering often the discrepancies in the modal data, i.e. the natural frequencies and the mode shapes, are minimised. In the minimisation problem, the objective function is formed by the 2-norm of the residual vector, containing the test/analysis differences in modal data. In the paper frequency residuals as well as mode shape residuals are formulated explicitly. The updating parameters are the uncertain physical properties of the structure (e.g. Young’s modulus,…), determined on elemental level. The optimisation problem is solved with the Trust Region Newton method which is an iterative sensitivity-based optimisation algorithm. The Gauss-Newton approximation is used to determine the Hessian of the objective function. Adjusting the model properties of all the elements in the FE model separately can result in a huge number of unknowns, which causes the sensitivity matrix to become ill-conditioned. Furthermore, a physically meaningful result is not guaranteed since all the elements are changed independently. Therefore, the use of damage functions is introduced and investigated in the paper. In this approach the global distribution of a model property is found by combining some global damage functions, each multiplied with its appropriate factor. These factors are the variables of the minimisation problem. The damage functions are determined by means of shape functions, known from FE theory. In a first approach only linear damage functions are used, but the method can be extended by including higher order functions. A clear improvement with regard to the general FEM Updating method is obtained, since the approach with damage functions reduces the number of updating parameters considerably and generates always a smooth distribution of the model property. Furthermore, the mathematical optimisation procedure can be easily adjusted by performing some simple matrix manipulations. The presented procedure is illustrated with a laboratory tested damaged reinforced concrete beam. The structural damage is represented by changes in the stiffness properties. A smooth and realistic damage pattern is identified with the updating method using damage functions. In the paper also the results obtained with the general method, i.e. by adjusting all finite elements separately, are given for comparison. References [1] Maia N.M.M., Silva J.M.M., He J., e.a., Theoretical and Experimental Modal Analysis. Research Studies Press Ltd., Somerset, England, 1997.